Calculating the Closest Distance between Catmull-Clark Subdivision Surfaces

J. N. Zhu, M. J. Wang, Z. C. Wei, B. Cao


In combination with divide-and-conquer strategy and multi-resolution sampling technology, a fast method for calculating the closest distance between Catmull-Clark subdivision surfaces is proposed. First, a data structure of subdivision surface is established to implement piecewise representation of subdivision surface. Based on divide-and-conquer strategy, the closest distance between subdivision surfaces can be obtained from closest distance calculation between subdivision surface patches. Second, based upon features of the topological structure of subdivision surface patch, the multi-resolution sampling method is established, with a method proposed for searching the vertex closest to a spatial point within the subdivision surface patches. Last, a method for searching the closest distance point pair between subdivision surfaces is established. The presented method is tested with examples to verify the feasibility and availability of the algorithm. The test result shows that this calculation method is more accurate and efficient.


Closest distance, Catmull-Clark subdivision surface, Divide and conquer, Multi-resolution Sampling.


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